Information on Result #676059
Linear OA(3249, 2223, F3, 52) (dual of [2223, 1974, 53]-code), using construction X applied to Ce(51) ⊂ Ce(45) based on
- linear OA(3239, 2187, F3, 52) (dual of [2187, 1948, 53]-code), using an extension Ce(51) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(33, 12, F3, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3249, 2219, F3, 2, 52) (dual of [(2219, 2), 4189, 53]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3249, 2219, F3, 3, 52) (dual of [(2219, 3), 6408, 53]-NRT-code) | [i] | ||
| 3 | Linear OOA(3249, 2219, F3, 4, 52) (dual of [(2219, 4), 8627, 53]-NRT-code) | [i] | ||
| 4 | Linear OOA(3249, 2219, F3, 5, 52) (dual of [(2219, 5), 10846, 53]-NRT-code) | [i] | ||
| 5 | Digital (197, 249, 2219)-net over F3 | [i] | ||
| 6 | Linear OOA(3249, 741, F3, 3, 52) (dual of [(741, 3), 1974, 53]-NRT-code) | [i] | OOA Folding | |